My Nana had a cat like yours. Sweet and loving to my grandma, but the most I ever saw of her was a blur of gray as she streaked under the bed or into a closet!
With Jasper's situation, it was more like trying to tame a juvenile wild wolf. I'm good with dogs. I figured I'd have him eating from my hand in a week at the most. And it took four years. He's a mighty force, though, you're right. He weighs 120 pounds and he's lean. (Kiara is getting a bit tubby in her old age, bless her.) Jasper has two escape hatches under the perimeter fence that I know of, and he goes out at night if he hears coyotes yipping in the distance and drives them farther. He's come back with a bit of blood on him a few times, but I honestly don't know if it was his or the coyotes'. They tend to circle and run in from behind while the dog is occupied with the one in front, and the times I did see blood, it was on his flanks, so I think maybe he got nipped once or twice.
Anyway, he's always back in time for breakfast, and if I happen to see him leaving for some reason, and call him, he ALWAYS comes back. That's unheard of with Pyrs. Once they're out and they have business to take care of, they don't generally pay much attention to us lowly two-legs. But he's a good boy. When Kiara was younger and could still "travel," they'd both sometimes get out, and they might be gone for days. Once they were gone for a week, and I was so pissed because what's the point of having a guardian dog if they're not home to guard? But Kiara doesn't go anywhere anymore, and Jasper always comes back to her. Now that he likes me, I think he'd still come back, even if Kiara wasn't here (but that's a thought I don't like to dwell on much).
I'm sorry I'm blathering on about these dogs, I just love them so much. They're my partners, they work 24 hours a day for nothing more than food and love, and we wouldn't be able to keep this farm running without them.